A.M.
I am a child care provider with an education in the field. I would begin to look for something before the baby is born, or you will be scrambling during your short time off with the baby. Many places do have waiting lists for infants.
If you are looking for family (home) care environment, ask if the caregiver is licensed and/or has an education or experience with children. See if she has all the appropriate facilities to care for your child and be sure she doesn't have more than two children under the age of 18mos. at one time. Request that she complete a sheet that tells you how/what your infant did that day, eg. diapering, sleeping, eating, etc. Also be sure that her house is completely child proof in all areas your child may be. She should have no more that six total children at one time. The home should be set up in a way that is child-friendly and has plenty of supplies and play things for children. She should provide learning activites for all children daily. Be sure to have a contract with your caregiver and ask that she she claim her income for your tax purposes and provide you with her tax ID and an end of the year receipt.
If you are looking for a center, ask if they are accredited by NAEYC, as this ensures they are providing the highest level of care and maintaining strict staffing standards, pratices, and ratios. Be sure that the facility is clean and that the caregivers have had backround checks (before they are permitted to work). The caregivers should appear friendly and kind. Set up a time to go visit and watch.